Hostname: page-component-7479d7b7d-wxhwt Total loading time: 0 Render date: 2024-07-12T03:24:36.325Z Has data issue: false hasContentIssue false
  • English
  • Français

Bound Sets in Partial Orders and the Fixed Point Property

Published online by Cambridge University Press:  20 November 2018

Hartmut Höft
Hartmut Höft*
Affiliation:
Dept. of Computer Science Eastern Michigan University Ypsilanti, MI 48197 Fachbereich Mathematik Universität Kaiserslautern 6750 Kaiserslautern
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper we introduce several properties closely related to the fixed point property of a partially ordered set P: the comparability property, the fixed point property for cones, and the fixed point extension property. We apply these properties to the sets of common bounds of the minimal (maximal) elements of the partially ordered set P in order to derive fixed point theorems for P.

Keywords

06A10
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 30 , Issue 4 , 01 December 1987 , pp. 421 - 428
Copyright
Copyright © Canadian Mathematical Society 1987

References

1. Baclawski, K. and Björner, A., Fixed points in partially ordered sets, Advances in Mathematics 31 (1979), pp. 263–287.Google Scholar
2. Davis, A., A characterization of complete lattices, Pacific J. Math. 5 (1955), pp. 311–319.Google Scholar
3. Duffus, D., Poguntke, W. and Rival, I., Retracts and the fixed point problem for finite partially ordered sets, Canad. Math. Bull. 23 (1980), pp. 231–236.Google Scholar
4. Höft, H. and Höft, M., Some fixed point theorems for partially ordered sets, Can. J. Math. 28 (1976), pp. 992–997.Google Scholar
5. Rival, I., The problem of fixed points in ordered sets, Annals of Discrete Math. 8 (1980), pp. 283–292.Google Scholar